Much of modern metrology and communication technology encodes information in electromagnetic waves, typically as an amplitude or phase. Although current hardware can perform near-ideal measurements ...of photon number or field amplitude, the ability to perform an ideal phase measurement is still lacking, even in principle. In this work, we implement a single-shot canonical phase measurement on a one-photon wave packet, which surpasses the current standard of heterodyne detection and is optimal for single-shot phase estimation. By applying quantum feedback to a Josephson parametric amplifier, our system adaptively changes its measurement basis during photon arrival and allows us to validate the detector’s performance by tracking the quantum state of the photon source. These results demonstrate that quantum feedback can both enhance the precision of a detector and enable it to measure new classes of physical observables.An adaptive heterodyne technique with a Josephson parametric amplifier detector allows a high-precision single-shot canonical phase measurement on a one-photon wave packet, complementing near-ideal measurements of photon number or field amplitude.
We show that the coherent interaction between free electrons and photons can be used for universal control of continuous-variable photonic quantum states in the form of Gottesman-Kitaev-Preskill ...(GKP) qubits. Specifically, we find that electron energy combs enable nondestructive measurements of the photonic state and can induce arbitrary gates. Moreover, a single electron interacting with multiple photonic modes can create highly entangled states such as Greenberger-Horne-Zeilinger states and cluster states of GKPs.
The Zeno effect, in which repeated observation freezes the dynamics of a quantum system, stands as an iconic oddity of quantum mechanics. When a measurement is unable to distinguish between states in ...a subspace, the dynamics within that subspace can be profoundly altered, leading to non-trivial behavior. Here we show that such a measurement can turn a non-interacting system with only single-qubit control into a two- or multi-qubit entangling gate, which we call a Zeno gate. The gate works by imparting a geometric phase on the system, conditioned on it lying within a particular nonlocal subspace. We derive simple closed-form expressions for the gate fidelity under a number of non-idealities and show that the gate is viable for implementation in circuit and cavity QED systems. More specifically, we illustrate the functioning of the gate via dispersive readout in both the Markovian and non-Markovian readout regimes, and derive conditions for longitudinal readout to ideally realize the gate.
In quantum mechanics, measurements cause wavefunction collapse that yields precise outcomes, whereas for non-commuting observables such as position and momentum Heisenberg's uncertainty principle ...limits the intrinsic precision of a state. Although theoretical work has demonstrated that it should be possible to perform simultaneous non-commuting measurements and has revealed the limits on measurement outcomes, only recently has the dynamics of the quantum state been discussed. To realize this unexplored regime, we simultaneously apply two continuous quantum non-demolition probes of non-commuting observables to a superconducting qubit. We implement multiple readout channels by coupling the qubit to multiple modes of a cavity. To control the measurement observables, we implement a 'single quadrature' measurement by driving the qubit and applying cavity sidebands with a relative phase that sets the observable. Here, we use this approach to show that the uncertainty principle governs the dynamics of the wavefunction by enforcing a lower bound on the measurement-induced disturbance. Consequently, as we transition from measuring identical to measuring non-commuting observables, the dynamics make a smooth transition from standard wavefunction collapse to localized persistent diffusion and then to isotropic persistent diffusion. Although the evolution of the state differs markedly from that of a conventional measurement, information about both non-commuting observables is extracted by keeping track of the time ordering of the measurement record, enabling quantum state tomography without alternating measurements. Our work creates novel capabilities for quantum control, including rapid state purification, adaptive measurement, measurement-based state steering and continuous quantum error correction. As physical systems often interact continuously with their environment via non-commuting degrees of freedom, our work offers a way to study how notions of contemporary quantum foundations arise in such settings.
We consider the effect of phase backaction on the correlator ⟨I(t)I(t+τ)⟩ for the output signal I(t) from continuous measurement of a qubit. We demonstrate that the interplay between informational ...and phase backactions in the presence of Rabi oscillations can lead to the correlator becoming larger than 1, even though |⟨I⟩|≤1. The correlators can be calculated using the generalized "collapse recipe," which we validate using the quantum Bayesian formalism. The recipe can be further generalized to the case of multitime correlators and arbitrary number of detectors, measuring non-commuting qubit observables. The theory agrees well with experimental results for continuous measurement of a transmon qubit. The experimental correlator exceeds the bound of 1 for a sufficiently large angle between the amplified and informational quadratures, causing the phase backaction. The demonstrated effect can be used to calibrate the quadrature misalignment.
The Zeno effect, in which repeated observation freezes the dynamics of a quantum system, stands as an iconic oddity of quantum mechanics. When a measurement is unable to distinguish between states in ...a subspace, the dynamics within that subspace can be profoundly altered, leading to non-trivial behavior. Here we show that such a measurement can turn a non-interacting system with only single-qubit control into a two- or multi-qubit entangling gate, which we call a Zeno gate. The gate works by imparting a geometric phase on the system, conditioned on it lying within a particular nonlocal subspace. We derive simple closed-form expressions for the gate fidelity under a number of non-idealities and show that the gate is viable for implementation in circuit and cavity QED systems. More specifically, we illustrate the functioning of the gate via dispersive readout in both the Markovian and non-Markovian readout regimes, and derive conditions for longitudinal readout to ideally realize the gate.
In quantum mechanics, measurements cause wavefunction collapse that yields precise outcomes, whereas for non-commuting observables such as position and momentum Heisenberg's uncertainty principle ...limits the intrinsic precision of a state. Although theoretical work1 has demonstrated that it should be possible to perform simultaneous non-commuting measurements and has revealed the limits on measurement outcomes, only recently2,3 has the dynamics of the quantum state been discussed. To realize this unexplored regime, we simultaneously apply two continuous quantum non-demolition probes of non-commuting observables to a superconducting qubit. We implement multiple readout channels by coupling the qubit to multiple modes of a cavity. To control the measurement observables, we implement a 'single quadrature' measurement by driving the qubit and applying cavity sidebands with a relative phase that sets the observable. Here, we use this approach to show that the uncertainty principle governs the dynamics of the wavefunction by enforcing a lower bound on the measurement-induced disturbance. Consequently, as we transition from measuring identical to measuring non-commuting observables, the dynamics make a smooth transition from standard wavefunction collapse to localized persistent diffusion and then to isotropic persistent diffusion. Although the evolution of the state differs markedly from that of a conventional measurement, information about both non-commuting observables is extracted by keeping track of the time ordering of the measurement record, enabling quantum state tomography without alternating measurements. Our work creates novel capabilities for quantum control, including rapid state purification4, adaptive measurement5,6, measurement-based state steering and continuous quantum error correction7. As physical systems often interact continuously with their environment via non-commuting degrees of freedom, our work offers a way8,9 to study how notions of contemporary quantum foundations10-14 arise in such settings.
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